论文标题
全空间形状优化的全空间方法
Full-Space Approach to Aerodynamic Shape Optimization
论文作者
论文摘要
空气动力学优化（ASO）涉及找到最佳表面，同时约束一组非线性偏微分方程（PDE）。传统方法使用在缩小空间中运行的准耐-牛顿方法，在每个设计步骤中，通过将流量求解器与优化器解耦来消除PDE约束。相反，全空间Lagrange-Newton-Krylov-Schur（LNK）通过同时最大程度地降低目标函数并提高PDE约束的可行性来融合设计和流动迭代，这需要更少的远期问题迭代。此外，使用二阶信息会导致许多设计迭代，而与控制变量的数量无关。我们讨论了建立有效的LNK ASO框架以及实施的复杂性的必要成分。然后，使用高阶不连续的Galerkin方法将LNK方法与基准二维测试案例上的缩小空间方法进行比较，以离散PDE约束。
Aerodynamic shape optimization (ASO) involves finding an optimal surface while constraining a set of nonlinear partial differential equations (PDE). The conventional approaches use quasi-Newton methods operating in the reduced-space, where the PDE constraints are eliminated at each design step by decoupling the flow solver from the optimizer. Conversely, the full-space Lagrange-Newton-Krylov-Schur (LNKS) approach couples the design and flow iteration by simultaneously minimizing the objective function and improving feasibility of the PDE constraints, which requires less iterations of the forward problem. Additionally, the use of second-order information leads to a number of design iterations independent of the number of control variables. We discuss the necessary ingredients to build an efficient LNKS ASO framework as well as the intricacies of their implementation. The LNKS approach is then compared to reduced-space approaches on a benchmark two-dimensional test case using a high-order discontinuous Galerkin method to discretize the PDE constraint.
